50 Years of the Golomb--Welch Conjecture
Information Theory
2020-06-25 v3 Combinatorics
math.IT
Abstract
Since 1968, when the Golomb--Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb--Welch conjecture. Further, new results on Golomb--Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given.
Keywords
Cite
@article{arxiv.1706.03589,
title = {50 Years of the Golomb--Welch Conjecture},
author = {Peter Horak and Dongryul Kim},
journal= {arXiv preprint arXiv:1706.03589},
year = {2020}
}
Comments
28 pages, 2 figures